Problem: A few families took a trip to an amusement park together. Tickets cost $$6.00$ each for adults and $$4.50$ each for kids, and the group paid $$58.50$ in total. There were $6$ fewer adults than kids in the group. Find the number of adults and kids on the trip.
Answer: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${6x+4.5y = 58.5}$ ${x = y-6}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-6}$ for $x$ in the first equation. ${6}{(y-6)}{+ 4.5y = 58.5}$ Simplify and solve for $y$ $ 6y-36 + 4.5y = 58.5 $ $ 10.5y-36 = 58.5 $ $ 10.5y = 94.5 $ $ y = \dfrac{94.5}{10.5} $ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into ${x = y-6}$ to find $x$ ${x = }{(9)}{ - 6}$ ${x = 3}$ You can also plug ${y = 9}$ into ${6x+4.5y = 58.5}$ and get the same answer for $x$ ${6x + 4.5}{(9)}{= 58.5}$ ${x = 3}$ There were $3$ adults and $9$ kids.